mixed-integer programming

Stochastic Programming Models for a Fleet Sizing and Appointment Scheduling Problem with Random Service and Travel Times

  • Shutian Li
  • Karmel S. Shehadeh
  • Man Yiu Tsang
    • Categories Applications - OR and Management Sciences, Scheduling, Stochastic Programming Tags , , , ,

    We propose a new stochastic mixed-integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following decision problems simultaneously: (i) a fleet sizing … Read more

    A polyhedral study of multivariate decision trees

  • Carla Michini
  • Zachary Zhou
    • Categories (Mixed) Integer Linear Programming, Data Science Theory, Polyhedra Tags , ,

    Decision trees are a widely used tool for interpretable machine learning. Multivariate decision trees employ hyperplanes at the branch nodes to route datapoints throughout the tree and yield more compact models than univariate trees. Recently, mixed-integer programming (MIP) has been applied to formulate the optimal decision tree problem. To strengthen MIP formulations, it is crucial … Read more

    Evaluating Mixed-Integer Programming Models over Multiple Right-hand Sides

  • Rachael M. Alfant
  • Temitayo Ajayi
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Linear Programming Tags , ,

    A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is not known exactly; however, there is no consensus metric for evaluating a MIP model when considering multiple right-hand sides. In … Read more

    Dynamic Rebalancing Optimization for Bike-sharing Systems: A Modeling Framework and Empirical Comparison

  • Jiaqi Liang
  • Sanjay Dominik Jena
  • Andrea Lodi
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Transportation Tags , , ,

    Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more

    Revisiting local branching with a machine learning lens

  • Defeng Liu
  • Matteo Fischetti
  • Andrea Lodi
    • Categories (Mixed) Integer Linear Programming, 0-1 Programming, Integer Programming Tags , ,

    Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution … Read more

    Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump

  • Timo Berthold
  • Gioni Mexi
  • Domenico Salvagnin
    • Categories (Mixed) Integer Linear Programming, 0-1 Programming Tags ,

    The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate … Read more

    Learning to Use Local Cuts

  • Timo Berthold
  • Matteo Francobaldi
  • Gregor Hendel
    • Categories (Mixed) Integer Linear Programming, Optimization Software Design Principles Tags , ,

    An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more

    PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming

  • Bo Tang
  • Elias B. Khalil
    • Categories Optimization Software and Modeling Systems Tags , ,

    In deterministic optimization, it is typically assumed that all parameters of the problem are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this … Read more

    Logic-based Benders decomposition with a partial assignment acceleration technique for avionics scheduling

  • Emil Karlsson
  • Elina Rönnberg
    • Categories (Mixed) Integer Linear Programming Tags , , , , ,

    Pre-runtime scheduling of large-scale electronic systems, as those in modern aircraft, can be computationally challenging. In this paper, we study a distributed integrated modular avionic system of practical relevance where the scheduling includes to assign communication messages to time slots and to sequence tasks on modules. For this problem, the challenge is the huge number … Read more